Multiple Extremal Integrals
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914296735203328 |
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| author | Bai, Shuyang Chen, Jiemiao |
| author_facet | Bai, Shuyang Chen, Jiemiao |
| contents | We introduce the notion of multiple extremal integrals as an extension of single extremal integrals, which have played important roles in extreme value theory. The multiple extremal integrals are formulated in terms of a product-form random sup measure derived from the $α$-Fréchet random sup measure. We establish a LePage-type representation similar to that used for multiple sum-stable integrals, which have been extensively studied in the literature. This approach allows us to investigate the integrability, tail behavior, and independence properties of multiple extremal integrals. Additionally, we discuss an extension of a recently proposed stationary model that exhibits an unusual extremal clustering phenomenon, now constructed using multiple extremal integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple Extremal Integrals Bai, Shuyang Chen, Jiemiao Probability 60G70 (Primary), 60F05 (Secondary) We introduce the notion of multiple extremal integrals as an extension of single extremal integrals, which have played important roles in extreme value theory. The multiple extremal integrals are formulated in terms of a product-form random sup measure derived from the $α$-Fréchet random sup measure. We establish a LePage-type representation similar to that used for multiple sum-stable integrals, which have been extensively studied in the literature. This approach allows us to investigate the integrability, tail behavior, and independence properties of multiple extremal integrals. Additionally, we discuss an extension of a recently proposed stationary model that exhibits an unusual extremal clustering phenomenon, now constructed using multiple extremal integrals. |
| title | Multiple Extremal Integrals |
| topic | Probability 60G70 (Primary), 60F05 (Secondary) |
| url | https://arxiv.org/abs/2503.23142 |